MULTIPLICATION OF VULGAR FRACTIONS.

198. To multiply fractions together.

RULE I. Multiply the numerators together for a numerator, and the denominators together for a denominator.

II. If the new fraction be a proper fraction, reduce it to its lowest terms; if an improper one, reduce it to its equivalent whole or mixed number".

I first multiply the numerators 3, 2, and 7 together, and the product is 42.

To multiply a fraction by a whole number, we must evidently multiply the numerator by the whole number; but to divide it, we must multiply the denominator by the whole number: thus, if be multiplied by 2, the pro

4

for two fourths are double of one fourth, and one eighth is the half of one

2

3

4

5

fourth this being premised, let it be required to multiply by now 2 multiplied by 4 equals 8; but it is not 2, but a third part of 2, which is to be

8

3

multiplied, and therefore the product will be the third part of 8 only, or ; but the multiplier is not 4, but the fifth part of 4 only, wherefore the product

the numerators multiplied together give the numerators of the product, and

the denominators multiplied give the denominators; which is the rule.

Then I multiply the denominators 4, 3, and 8 together, and the product is 9

199. When mixed numbers or complex fractions are to be

multiplied.

RULE. Reduce the mixed numbers to improper fractions, and the complex fractions to simple ones, and proceed as before.

The reason of this process evidently follows from the preceding note.

and

15

ber 330.

15'

Thirdly, I multiply the two fractions

2

together, and reduce the product to its equivalent mixed num

1

14

7

91

30

200. To multiply a whole number and fraction together.

RULE. Multiply the numerator of the fraction by the whole number, and under the product set the denominator; then reduce this fraction to its lowest or proper terms, as the case requires, and it will be the answero.

e Whatever parts a fraction consists of, its product when multiplied by any whole number will consist of like parts; thus two sevenths multiplied by three

201. When the whole number will divide the denominator of the fraction without remainder, divide by it, and set the quotient under the given numerator; this fraction reduced as before will give the answer".

a To divide the denominator by any number is the same as to multiply the

2, making the resulting fraction the same as by the former method; and

2

the same holds true in every other instance: wherefore the truth of the rule is manifest.

202. When a numerator and denominator are the same, both ay be omitted in the operation, a small line being drawn rough the figures omitted; this operation is called cancel

The numerator of a fraction may be considered as a multiplier, and the lenominator as a divisor; it is plain, that if any number be both multiplied and divided by any (the same) number, the result will be the same as the iven number; wherefore such multiplication and division (as they muually destroy the effect of each other) may be omitted: which is what the rule irects.

It may be further observed, that one numerator cancels only one equal denominator, and vice versa; but it will cancel two or more when it is equal to heir product: thus, in ex. 26. the numerator 4 cancels the denominator 4 only, but the denominator 6 cancels both the numerators 2 and 3, because it equals 2 x 3.